Learn Dutch: De vervaagde achtergrond geeft een rustig effect. - The blurred background gives a calm effect.

This is about keeping the long A sound. In the infinitive vervagen, the A is at the end of an open syllable (ver-va-gen), which naturally makes the vowel long. When we add the -e to the past participle vervaagd, the word breaks into syllables between the two consonants (ver-vaag-de). Because the A is now in a closed syllable ending in G, we have to write a double aa to prevent it from becoming a short A sound.

How exactly is the past participle vervaagde formed from the verb?

First, you form the standard past participle. The stem of vervagen is vervaag. Because the letter G is not in the consonant memory aid 't kofschip, you add a D, giving you vervaagd. Then, because it is used as an adjective before the de-word achtergrond, you add the standard -e adjective ending, resulting in vervaagde.

Why doesn't rustig get an -e ending here, even though vervaagde does?

Normally, adjectives before a noun get an -e ending, which is why we have de vervaagde achtergrond. The major exception is for singular het-words preceded by een, geen, or no article at all. Because effect is a het-word, the adjective drops the -e after een, making it een rustig effect.